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  • 1.
    Abdeljawad, Ahmed
    et al.
    Univ Turin, Italy.
    Cappiello, Marco
    Univ Turin, Italy.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Pseudo-Differential Calculus in Anisotropic Gelfand-Shilov Setting2019In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 91, no 3, article id UNSP 26Article in journal (Refereed)
    Abstract [en]

    We study some classes of pseudo-differential operators with symbols a admitting anisotropic exponential type growth at infinity. We deduce mapping properties for these operators on Gelfand-Shilov spaces. Moreover, we deduce algebraic and certain invariance properties of these classes.

  • 2.
    Abdeljawad, Ahmed
    et al.
    University of Turin, Italy.
    Coriasco, Sandro
    University of Turin, Italy.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Liftings for ultra-modulation spaces, and one-parameter groups of Gevrey-type pseudo-differential operators2020In: Analysis and Applications, ISSN 0219-5305, E-ISSN 1793-6861 , Vol. 18, no 4, p. 523-583Article in journal (Refereed)
    Abstract [en]

    We deduce one-parameter group properties for pseudo-differential operators Op(a), where a belongs to the class Λ∗(ω0) of certain Gevrey symbols. We use this to show that there are pseudo-differential operators Op(a) and Op(b) which are inverses to each other, where a ∈ Λ∗(ω0) and b ∈ Λ∗(1/ω0). We apply these results to deduce lifting property for modulation spaces and construct explicit isomorphisms between them. For each weight functions ω,ω0 moderated by GRS submultiplicative weights, we prove that the Toeplitz operator (or localization operator) Tp(ω0) is an isomorphism from Mp,q(ω) to M(ω/ω0)p,q for every p,q ∈(0,∞]. © 2019 World Scientific Publishing Company.

  • 3.
    Abdeljawad, Ahmed
    et al.
    Austrian Acad Sci, Austria.
    Fernandez, Carmen
    Univ Valencia, Spain.
    Galbis, Antonio
    Univ Valencia, Spain.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Uster, Ruya
    Istanbul Univ, Turkey.
    Characterizations of a class of Pilipovic spaces by powers of harmonic oscillator2020In: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, ISSN 1578-7303, Vol. 114, no 3, p. 1-13, article id 131Article in journal (Refereed)
    Abstract [en]

    We show that a smooth function f on Rd belongs to the Pilipovic space H (Rd ) or the Pilipovic space H0,bσ (Rd ), if and only if the Lp norm of HN d f for N ≥ 0, satisfy certain types of estimates. Here Hd = |x|2 − Δx is the harmonic oscillator.

  • 4.
    Abdeljawad, Ahmed
    et al.
    University of Turin, Italy.
    Toft, Joachim
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Anisotropic Gevrey-Hörmander Pseudo-Differential Operators on Modulation Spaces2020In: Advances in Microlocal and Time-Frequency Analysis / [ed] P. Boggiatto, M. Cappiello, E. Cordero, S. Coriasco, G. Garello, A. Oliaro, J. Seiler, Birkhäuser Verlag, 2020, p. 1-20Chapter in book (Refereed)
  • 5.
    Abdullahu, Albinota
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Imsirovic, Elma
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Olika strategier inom bråk för att bidra till utvecklad kunskapsutveckling hos elever i grundskolan: Systematisk litteraturstudie2023Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
  • 6.
    Abdullahu, Albinota
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Imsirovic, Elma
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    To navigate through linguistic barriers: An empirical study of problem- solving in mathematics among students with Swedish as second language2024Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Denna studie syftar till att undersöka och identifiera svårigheter som andraspråkselever möter i undervisningen i koppling till problemlösningsuppgifter med fokus på bråkräkning. Studien syftar även till elevers generella upplevelser kring problemlösning med bråk. För att uppnå detta genomfördes ett test med problemlösningsuppgifter som involverar bråk. Testet genomfördes på två olika skolor för att jämföra resultat mellan olika elevgrupper. Genom denna jämförelse strävar vi efter att identifiera eventuella skillnader i prestation och förståelse samt att belysa vilka faktorer som kan påverka andraspråkselevers framgång i matematiska problem. Studien avser att bidra till en djupare förståelse av de utmaningar och möjligheter som andraspråkselever står inför i matematikundervisningen. Resultatet visar att problemlösning med bråk påverkar andraspråkselever på olika sätt där språket utgör ett hinder för förståelse och uträkning.

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  • 7.
    Abidi, Hani
    et al.
    Esprit School of Business, Tunisia.
    Amami, Rim
    Imam Abdulrahman Bin Faisal University, Saudi Arabia.
    Pettersson, Roger
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Trabelsi, Chiraz
    Centre Universitaire de Mayotte, France;IMAG Montpellier, France.
    L2-convergence of Yosida approximation for semi-linear backward stochastic differential equation with jumps in infinite dimension2024In: Arab Journal of Mathematical Sciences, ISSN 1319-5166Article in journal (Refereed)
    Abstract [en]

    Purpose: The main motivation of this paper is to present  the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.

    Design/methodology/approach: The authors establish a result concerning the L2-convergence rate of the solution of backward stochastic differential equation with jumps with respect to the Yosida approximation.

    Findings: The authors carry out a convergence rate of Yosida approximation to the semi-linear backward stochastic differential equation in infinite dimension.

    Originality/value: In this paper, the authors present the Yosida approximation of a semi-linear backward stochastic differential equation in infinite dimension. Under suitable assumption and condition, an L2-convergence rate is established.

  • 8.
    Abidi, Hani
    et al.
    Esprit Sch Business, Tunisia.
    Oualaid, Abdelkarim
    Cadi Ayyad Univ, Morocco.
    Ouknine, Youssef
    Cadi Ayyad Univ, Morocco;Mohammed VI Polytech Univ, Morocco.
    Pettersson, Roger
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    A mild approach to spatial discretization for backward stochastic differential equations in infinite dimensions2024In: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 42, no 2, p. 98-120Article in journal (Refereed)
    Abstract [en]

    In this paper, we present the stability result of a spatial semi-discrete scheme to backward stochastic differential equations taking values in a Hilbert space. Under suitable assumptions of the final value and the drift, a convergence rate is established.

  • 9.
    Abidi, Hani
    et al.
    Univ Tunis El Manar, Tunisia.
    Pettersson, Roger
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Spatial convergence for semi-linear backward stochastic differential equations in Hilbert space: a mild approach2020In: Computational and Applied Mathematics, ISSN 2238-3603, E-ISSN 1807-0302, Vol. 39, no 2, p. 1-11, article id 94Article in journal (Refereed)
    Abstract [en]

    In this paper, we present convergence results of a spatial semi-discrete approximation of a Hilbert space-valued backward stochastic differential equations with noise driven by a cylindrical Q-Wiener process. Both the solution and its space discretization are formulated in mild forms. Under suitable assumptions of the final value and the drift, a convergence rate is established.

  • 10.
    Accardi, Luigi
    et al.
    Univ Rome Torvergata, Italy.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ohya, Masanori
    Tokyo Univ Sci, Japan.
    Tanaka, Yoshiharu
    Tokyo Univ Sci, Japan.
    Yamato, Ichiro
    Tokyo Univ Sci, Japan.
    Application of Non-Kolmogorovian Probability and Quantum Adaptive Dynamics to Unconscious Inference in Visual Perception Process2016In: Open systems & information dynamics, ISSN 1230-1612, E-ISSN 1573-1324, Vol. 23, no 2, article id 1650011Article in journal (Refereed)
    Abstract [en]

    Recently a novel quantum information formalism - quantum adaptive dynamics - was developed and applied to modelling of information processing by bio-systems including cognitive phenomena: from molecular biology (glucose-lactose metabolism for E.coli bacteria, epigenetic evolution) to cognition, psychology. From the foundational point of view quantum adaptive dynamics describes mutual adapting of the information states of two interacting systems (physical or biological) as well as adapting of co-observations performed by the systems. In this paper we apply this formalism to model unconscious inference: the process of transition from sensation to perception. The paper combines theory and experiment. Statistical data collected in an experimental study on recognition of a particular ambiguous figure, the Schroer stairs, support the viability of the quantum(-like) model of unconscious inference including modelling of biases generated by rotation-contexts. From the probabilistic point of view, we study (for concrete experimental data) the problem of contextuality of probability, its dependence on experimental contexts. Mathematically contextuality leads to non-Komogorovness: probability distributions generated by various rotation contexts cannot be treated in the Kolmogorovian framework. At the same time they can be embedded in a "big Kolmogorov space" as conditional probabilities. However, such a Kolmogorov space has too complex structure and the operational quantum formalism in the form of quantum adaptive dynamics simplifies the modelling essentially.

  • 11.
    ACHEK, JENNIE ANNA
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Växjö Islamiska skola.
    Berglund, Elin
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Språkstörning i Matematikens Värld: En studie i hur speciallärare i matematik arbetar språkutvecklande med elever med speciella utbildningsbehov i matematik som samtidigt har språkstörning.2023Independent thesis Advanced level (professional degree), 60 credits / 90 HE creditsStudent thesis
    Abstract [sv]

    Syftet med vår studie är att bidra med kunskap om på vilket sätt speciallärare arbetar språkutvecklande med elever med speciella utbildningsbehov i matematik och som samtidigt har språkstörning. Tidigare forskning visar att språkstörning har stor inverkan på elevers kunskpasinhämtning i matematik om de samtidigt har SUM. Studien genomfördes med semistrukturerade djupintervjuer, Resultaten har bearbetats mot tidigare forskning. Vi fann att alla speciallärare vi intervjuat arbetatde på ett språkutvecklande sätt i matematikundervisningen. Trots att speciallärarna hade olika kunskap om språkstörning arbetade de alla på liknande sätt med språkutveckling i matematiken.

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  • 12.
    Adenier, Guillaume
    et al.
    INRiM, Italy.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Test of the no-signaling principle in the Hensen loophole-free CHSH experiment2017In: Fortschritte der Physik, ISSN 0015-8208, E-ISSN 1521-3978, Vol. 65, no 9, article id 1600096Article in journal (Refereed)
    Abstract [en]

    We analyze the data from the loophole-free CHSH experiment performed by Hensen et al., and show that it is actually not exempt of an important loophole. By increasing the size of the sample of event-ready detections, one can exhibit in the experimental data a violation of the no-signaling principle with a statistical significance at least similar to that of the reported violation of the CHSH inequality, if not stronger. The data from the loophole-free CHSH experiment performed by Hensen et al. are analysed, It is shown that it is actually not exempt of an important loophole. By increasing the size of the sample of event-ready detections, one can exhibit in the experimental data a violation of the no-signaling principle with a statistical significance at least similar to that of the reported violation of the CHSH inequality, if not stronger.

  • 13.
    Adenier, Guillaume
    et al.
    University of Oslo, Norway.
    Watanabe, Noboru
    Tokyo University of Science, Japan.
    Basieva, Irina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Multiple-photon absorption attack on entanglement-based quantum key distribution protocols2013In: Quantum Bio-Informatics V: Proceedings of the Quantum Bio-Informatics 2011 : Tokyo University of Science, Japan, 7 – 12 March 2011 / [ed] Luigi Accardi, Wolfgang Freudenberg, Masanori Ohya, Singapore: World Scientific, 2013, Vol. 30, p. 171-180Conference paper (Refereed)
    Abstract [en]

    We propose a multiple-photon absorption attack on Quantum Key Distribution protocols. In this attack, the eavesdropper (Eve) is in control of the source and sends pulses correlated in polarization (but not entangled) containing several photons at frequencies for which only multiple-photon absorptions are possible in Alice's and Bob's detectors. Whenever the number of photons from one pulse are dispatched in insufficient number to trigger a multiple-photon absorption in either channel, the pulse remains undetected. We show that this simple feature is enough to reproduce the type of statistics on the detected pulses that are considered as indicating a secure quantum key distribution in entangled-based protocols, even though the source is controlled by Eve, and we discuss possible countermeasures.

  • 14.
    Adolfsson, Rebekka
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Zetterlund, Ulrika
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Singaporematematik ur ett specialpedagogiskt perspektiv: Lärares beskrivning av arbetet med Singaporematematik2022Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Denna kvalitativa studie, med en tematisk analys av nio lärares beskrivningar av Singaporematematik, har som syfte att redogöra för lärares erfarenheter ur ett specialpedagogiskt perspektiv och vad Singaporematematiken kan tillföra den specialpedagogiska verksamheten. Metoden har varit semistrukturerade intervjuer och urvalet har skett genom redan tidigare kända kontakter med kriteriet att lärarna ska ha erfarenhet av att arbeta med Singaporematematik och elever i matematiksvårigheter. Urvalsmetoden kan benämnas som snöbollsurval. Analysen av resultatet visar att lärarna i huvudsak beskriver sin undervisning ur ett relationellt perspektiv med kategoriska inslag. Lärarnas engagemang och intresse för undervisning, matematik och elevers lärande är det som i grunden är viktigt. När lärarna beskriver synen på elevernas lärande visar resultatet att Singaporematematik enligt analysen kan leda till djupare förståelse, ökad motivation och engagemang hos eleverna. Blockmodellen förklaras som ett visuellt verktyg som lärarna beskriver kan fungera som en hjälp för eleverna i bryggan mellan det konkreta och det abstrakta. Vår slutsats är att Singaporematematik kan tillföra den specialpedagogiska verksamheten en tydlig struktur, ökad kommunikation i klassrummet, gemensamt lärande, differentierad undervisning och stöd för eleverna att vandra mellan olika representationsformer. Dock behöver inte denna undervisning benämnas Singaporematematik och undervisningen behöver inte vara kopplat till något speciellt läromedel.

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  • 15.
    Adolfsson, Tea
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Nilsson, Linnéa
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Molazem Ehtesham Olsson, Nadja
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Jag blir motiverad när...: En kvantitativ studie om vilka multiplikationsmetoder som motiverar elever i årskurs 52020Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Den här empiriska forskningsrapporten riktar in sig på vilka metoder samt vilka inre och yttre faktorer som motiverar elever till att träna multiplikation. Undersökningen har genomförts på två skolor i årskurs 5. Forskningsmetoden som tillämpats för att besvara frågeställningarna är av kvantitativ karaktär och utgörs av en enkät. Syftet med enkäten var att lyfta fram vilka metoder som är mest motiverande för eleverna när de räknar multiplikation samt vilka faktorer som bidrar till motivationen. Resultatet visade att metoderna digitala verktyg och algoritm motiverade eleverna i en större utsträckning än övriga metoder som efterfrågades. I resultatet framgår det av eleverna att de inre motivationsfaktorerna är av större betydelse än de yttre när de räknar multiplikation. Det visar sig också finnas ett visst samband mellan metoderna och den inre motivationen.

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  • 16.
    Aerts, Diederik
    et al.
    Brussels Free University, Belgium.
    Khrennikov, AndreiLinnaeus University, Faculty of Technology, Department of Mathematics.Melucci, MassimoUniversity of Padova, Italy.Bourama, ToniHoward University, USA.
    Quantum-Like Models for Information Retrieval and Decision-Making2019Collection (editor) (Refereed)
    Abstract [en]

    Recent years have been characterized by tremendous advances in quantum information and communication, both theoretically and experimentally. In addition, mathematical methods of quantum information and quantum probability have begun spreading to other areas of research, beyond physics. One exciting new possibility involves applying these methods to information science and computer science (without direct relation to the problems of creation of quantum computers). 

    The aim of this Special Volume is to encourage scientists, especially the new generation (master and PhD students), working in computer science and related mathematical fields to explore novel possibilities based on the mathematical formalisms of quantum information and probability.  The contributing authors, who hail from various countries, combine extensive quantum methods expertise with real-world experience in application of these methods to computer science. The problems considered chiefly concern quantum information-probability based modeling in the following areas: information foraging; interactive quantum information access; deep convolutional neural networks; decision making, quantum dynamics; open quantum systems; and theory of contextual probability. 

    The book offers young scientists (students, PhD, postdocs) an essential introduction to applying the mathematical apparatus of quantum theory to computer science, information retrieval, and information processes. 

  • 17.
    Aghababa, Somayeh
    Linnaeus University, Faculty of Engineering and Technology, Department of Mathematics.
    Extremal dependency:The GARCH(1,1) model and an Agent based model2013Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    This thesis focuses on stochastic processes and some of their properties are investigated which are necessary to determine the tools, the extremal index and the extremogram. Both mathematical tools measure extremal dependency within random time series. Two different models are introduced and related properties are discussed. The probability function of the Agent based model is surveyed explicitly and strong stationarity is proven. Data sets for both processes are simulated and clustering of the data is investigated with two different methods. Finally an estimation of the extremogram is used to interpret dependency of extremes within the data.

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  • 18.
    Agram, Nacira
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Stochastic optimal control of McKean-Vlasov equations with anticipating law2019In: Afrika Matematika, ISSN 1012-9405, E-ISSN 2190-7668, Vol. 30, no 5-6, p. 879-901Article in journal (Refereed)
    Abstract [en]

    We are interested in Pontryagin’s stochastic maximum principle of controlled McKean–Vlasov stochastic differential equations. We allow the law to be anticipating, in the sense that, the coefficients (the drift and the diffusion coefficients) depend not only of the solution at the current time t, but also on the law of the future values of the solution PX(t+δ)" role="presentation">PX(t+δ), for a given positive constant δ" role="presentation">δ. We emphasise that being anticipating w.r.t. the law of the solution process does not mean being anticipative in the sense that it anticipates the driving Brownian motion. As an adjoint equation, a new type of delayed backward stochastic differential equations (BSDE) with implicit terminal condition is obtained. By using that the expectation of any random variable is a function of its law, our BSDE can be written in a simple form. Then, we prove existence and uniqueness of the solution of the delayed BSDE with implicit terminal value, i.e. with terminal value being a function of the law of the solution itself.

  • 19.
    Agram, Nacira
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Choutri, Salah Eddine
    New York Univ Abu Dhabi, United Arab Emirates.
    Mean-field FBSDE and optimal control2021In: Stochastic Analysis and Applications, ISSN 0736-2994, E-ISSN 1532-9356, Vol. 39, no 2, p. 235-251Article in journal (Refereed)
    Abstract [en]

    We study optimal control for mean-field forward-backward stochastic differential equations with payoff functionals of mean-field type. Sufficient and necessary optimality conditions in terms of a stochastic maximum principle are derived. As an illustration, we solve an optimal portfolio with mean-field risk minimization problem.

  • 20.
    Agram, Nacira
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Djehiche, Boualem
    KTH Royal instute of technology, Sweden.
    On a class of reflected backward stochastic Volterra integral equations and related time-inconsistent optimal stopping problems2021In: Systems & control letters (Print), ISSN 0167-6911, E-ISSN 1872-7956, Vol. 155, article id 104989Article in journal (Refereed)
    Abstract [en]

    We introduce a class of one-dimensional continuous reflected backward stochastic Volterra integral equations driven by Brownian motion, where the reflection keeps the solution above a given stochastic process (lower obstacle). We prove existence and uniqueness by a fixed point argument and derive a comparison result. Moreover, we show how the solution of our problem is related to a time-inconsistent optimal stopping problem and derive an optimal strategy. 

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  • 21.
    Agram, Nacira
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Haadem, Sven
    Univ Oslo, Norway.
    Øksendal, Bernt
    Univ Oslo, Norway.
    Proske, Frank
    Univ Oslo, Norway.
    Optimal Stopping, Randomized Stopping, and Singular Control with General Information Flow2022In: Theory of Probability and its Applications, ISSN 0040-585X, E-ISSN 1095-7219, Vol. 66, no 4, p. 601-612Article in journal (Refereed)
    Abstract [en]

    The purpose of this paper is twofold. First, we extend the well-known relation between optimal stopping and randomized stopping of a given stochastic process to a situation where the available information flow is a filtration with no a priori assumed relation to the filtration of the process. We call these problems optimal stopping and randomized stopping with general information. we introduce a special singular stochastic control problem with general information and show that this is also equivalent to the partial information optimal stopping and randomized stopping problems. Then we show that the solution of this singular control problem can be expressed in terms of partial information variational inequalities.

  • 22.
    Agram, Nacira
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Haadem, Sven
    University of Oslo, Norway.
    Øksendal, Bernt
    University of Oslo, Norway.
    Proske, Frank
    University of Oslo, Norway.
    Optimal stopping, randomized stopping and singular control with partial information flowManuscript (preprint) (Other academic)
    Abstract [en]

    The purpose of this paper is two-fold: We extend the well-known relation between optimal stopping and randomized stopping of a given stochastic process to a situation where the available information flow is a sub-filtration of the filtration of the process. We call these problems optimal stopping and randomized stopping with partial information. Following an idea of Krylov [K] we introduce a special singular stochastic control problem with partial information and show that this is also equivalent to the partial information optimal stopping and randomized stopping problems. Then we show that the solution of this singular control problem can be expressed in terms of (partial information) variational inequalities, which in turn can be rewritten as a reflected backward stochastic differential equation (RBSDE) with partial information.

  • 23.
    Agram, Nacira
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Hilbert, Astrid
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Øksendal, Bernt
    University of Oslo, Norway.
    Singular control of SPDEs with space-mean dynamics2020In: Mathematical Control & Related Fields, ISSN 2156-8472, Vol. 10, no 2, p. 425-441Article in journal (Refereed)
    Abstract [en]

    We consider the problem of optimal singular control of a stochastic partial differential equation (SPDE) with space-mean dependence. Such systems are proposed as models for population growth in a random environment. We obtain sufficient and necessary maximum principles for such control problems. The corresponding adjoint equation is a reflected backward stochastic partial differential equation (BSPDE) with space-mean dependence. We prove existence and uniqueness results for such equations. As an application we study optimal harvesting from a population modelled as an SPDE with space-mean dependence.

  • 24.
    Agram, Nacira
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. University Med Khider, Algeria.
    Hu, Yaozhong
    University of Alberta, Canada;University of Oslo, Norway.
    Øksendal, Bernt
    University of Oslo, Norway.
    Mean-field backward stochastic differential equations and applicationsManuscript (preprint) (Other academic)
    Abstract [en]

    In this paper we study the mean-field backward stochastic differential equations (mean-field bsde) of the form

    dY (t) = −f(t, Y (t), Z(t), K(t, ·), E[ϕ(Y (t), Z(t), K(t, ·))])dt + Z(t)dB(t) + R R0 K(t, ζ)N˜(dt, dζ),

    where B is a Brownian motion, N˜ is the compensated Poisson random measure. Under some mild conditions, we prove the existence and uniqueness of the solution triplet (Y, Z, K). It is commonly believed that there is no comparison theorem for general mean-field bsde. However, we prove a comparison theorem for a subclass of these equations.When the mean-field bsde is linear, we give an explicit formula for the first component Y (t) of the solution triplet. Our results are applied to solve a mean-field recursive utility optimization problem in finance.

  • 25.
    Agram, Nacira
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Oksendal, Bernt
    Univ Oslo, Norway.
    A financial market with singular drift and no arbitrage2021In: Mathematics and Financial Economics, ISSN 1862-9679, E-ISSN 1862-9660, Vol. 15, p. 477-500Article in journal (Refereed)
    Abstract [en]

    We study a financial market where the risky asset is modelled by a geometric Ito-Levy process, with a singular drift term. This can for example model a situation where the asset price is partially controlled by a company which intervenes when the price is reaching a certain lower barrier. See e.g. Jarrow and Protter (J Bank Finan 29:2803-2820, 2005) for an explanation and discussion of this model in the Brownian motion case. As already pointed out by Karatzas and Shreve (Methods of Mathematical Finance, Springer, Berlin, 1998) (in the continuous setting), this allows for arbitrages in the market. However, the situation in the case of jumps is not clear. Moreover, it is not clear what happens if there is a delay in the system. In this paper we consider a jump diffusion market model with a singular drift term modelled as the local time of a given process, and with a delay theta>0 in the information flow available for the trader. We allow the stock price dynamics to depend on both a continuous process (Brownian motion) and a jump process (Poisson random measure). We believe that jumps and delays are essential in order to get more realistic financial market models. Using white noise calculus we compute explicitly the optimal consumption rate and portfolio in this case and we show that the maximal value is finite as long as theta>0. This implies that there is no arbitrage in the market in that case. However, when theta goes to 0, the value goes to infinity. This is in agreement with the above result that is an arbitrage when there is no delay. Our model is also relevant for high frequency trading issues. This is because high frequency trading often leads to intensive trading taking place on close to infinitesimal lengths of time, which in the limit corresponds to trading on time sets of measure 0. This may in turn lead to a singular drift in the pricing dynamics. See e.g. Lachapelle et al. (Math Finan Econom 10(3):223-262, 2016) and the references therein.

  • 26.
    Agram, Nacira
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Oksendal, Bernt
    University of Oslo, Norway.
    Introduction to White Noise, Hida-Malliavin Calculus and ApplicationsManuscript (preprint) (Other academic)
    Abstract [en]

    The purpose of these lectures is threefold: We first give a short survey of the Hida white noise calculus, and in this context we introduce the Hida-Malliavin derivative as a stochastic gradient with values in the Hida stochastic distribution space (S. We show that this Hida-Malliavin derivative defined on L2(FT,P) is a natural extension of the classical Malliavin derivative defined on the subspace D1,2 of L2(P). The Hida-Malliavin calculus allows us to prove new results under weaker assumptions than could be obtained by the classical theory. In particular, we prove the following: (i) A general integration by parts formula and duality theorem for Skorohod integrals, (ii) a generalised fundamental theorem of stochastic calculus, and (iii) a general Clark-Ocone theorem, valid for all F∈L2(FT,P). As applications of the above theory we prove the following: A general representation theorem for backward stochastic differential equations with jumps, in terms of Hida-Malliavin derivatives; a general stochastic maximum principle for optimal control; backward stochastic Volterra integral equations; optimal control of stochastic Volterra integral equations and other stochastic systems.

  • 27.
    Agram, Nacira
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics. Univ Oslo, Norway.
    Oksendal, Bernt
    Univ Oslo, Norway.
    Mean-field stochastic control with elephant memory in finite and infinite time horizon2019In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 91, no 7, p. 1041-1066Article in journal (Refereed)
    Abstract [en]

    Our purpose of this paper is to study stochastic control problems for systems driven by mean-field stochastic differential equations with elephant memory, in the sense that the system (like the elephants) never forgets its history. We study both the finite horizon case and the infinite time horizon case. In the finite horizon case, results about existence and uniqueness of solutions of such a system are given. Moreover, we prove sufficient as well as necessary stochastic maximum principles for the optimal control of such systems. We apply our results to solve a mean-field linear quadratic control problem. For infinite horizon, we derive sufficient and necessary maximum principles. As an illustration, we solve an optimal consumption problem from a cash flow modelled by an elephant memory mean-field system.

  • 28.
    Ahlgren Veinfors, Elin
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Lang, Karolina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Andersson, Malin
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Matematisk fallenhet, problemlösning och motivation: En systematisk litteraturstudie om hur problemlösning kan motivera elever med matematisk fallenhet2019Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I denna systematiska litteraturstudie fokuseras elever med fallenhet för matematik, problemlösning samt motivation och sambanden mellan dessa. Syftet med studien är att kartlägga hur elever med matematisk fallenhet kan utmärka sig, att undersöka hur problemlösning kan utmana och utveckla dessa elever samt att undersöka sambanden mellan elever med matematisk fallenhet, problemlösning och motivation. För att besvara studiens syfte samt frågeställningar baseras studien på ett flertal vetenskapliga publikationer som har analyserats utifrån tre teoretiska perspektiv. Studiens resultatanalys visar på flera utmärkande drag hos elever med matematisk fallenhet, vissa mer förekommande än andra. Resultatanalysen i studien redogör även för kännetecken för problemlösningsuppgifter, med vilka faser en problemlösningsuppgift kan lösas samt hur arbete med problemlösning kan bidra till utmaning och fortsatt utveckling hos elever med matematisk fallenhet. Avslutningsvis redogör studiens resultatanalys för sambandet mellan elever med matematisk fallenhet, problemlösning och motivation. Studien visar att motivationen hos elever med matematisk fallenhet ökar vid arbete med problemlösning.

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  • 29.
    Ahmed, Abdirauf
    Linnaeus University, Faculty of Technology, Department of Mathematics. Migrationsverket.
    Describing and modelling the flow of the migration process with simple queueing systems.2018Independent thesis Basic level (degree of Bachelor), 180 HE creditsStudent thesis
    Abstract [en]

     The aim of this thesis is to apply M/M/1 and M/M/2 queueing system models

    to student and working visas applicants. From empirically observed arrival times and

    departure times, the arrival and service intensities are estimated. It is obtained that

    the estimated service intensities are essentially double for the M/M/1 queueing model

    compared to the M/M/2 model. Hence, the estimated trac intensities, as they are

    dened in this thesis, are almost the same here, and close to one. Furthermore, the

    empirical distribution of the time in the system for the student visas seems to be

    surprisingly well approximated by the theoretical ones obtained from the M/M/1 and

    M/M/2 models.

    The total time in the system for the two models are almost the same, while for

    the M/M/2 model the service times are about the double of the service times of the

    M/M/1 model which is compensated by shorter waiting times for the M/M/2 queue.

    Therefore, there is a struggle in modelling between having a quicker service time with

    less servers or a shorter waiting time period with more servers.

    Modelling of the total time in the system, which is the important time for the

    applicant and is as well the observed one, seems to be indierent to whether it is

    M/M/1 modelling or M/M/2 modelling. That indierence is explained by the fact

    that the estimated trac intensity is close to one.

    A major consideration is that there is a \wall" eect of the data. The \wall" eect

    arises from the ratio of the uncompleted and completed changes towards the end of

    year 2017. In this thesis the \wall" eect is resolved by removing the last data.

    2

  • 30. Aksimsek, Sinan
    et al.
    Cinar, Gökhan
    Nilsson, Börje
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Nordebo, Sven
    Linnaeus University, Faculty of Technology, Department of Physics and Electrical Engineering.
    TEM wave scattering by a step discontinuity on the outer wall of a coaxial waveguide2013In: IEEE transactions on microwave theory and techniques, ISSN 0018-9480, E-ISSN 1557-9670, Vol. 61, no 8, p. 2783-2791Article in journal (Refereed)
    Abstract [en]

    In this paper, the propagation of TEM waves along a coaxial waveguide with a step discontinuity on its outer wall is investigated rigorously by applying the direct Fourier transform and reducing the problem into the solution of a modified Wiener–Hopf equation. The solution for the field terms are determined in terms of an infinite number of unknown coefficients, which satisfy an infinite set of linear algebraic equations. These equations are solved numerically and the effect of area ratio is presented graphically at the end of the analysis. The same problem is also analyzed by applying the mode-matching technique and the results of the two approaches are compared. It is observed numerically that the Wiener–Hopf technique provides a better convergence than the mode-matching technique.

  • 31.
    Alexandersson, Mikaela
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Samuelsson, Emelie
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Variation i geometriundervisning: En studie med fokus på tredimensionella objekt2019Student paper other, 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Studien är en kvalitativ studie med fokus på hur tredimensionella objekt framställs och arbetas med i matematikundervisningen. Syftet med denna studie är att undersöka hur lärare varierar undervisningsmetoder i undervisningen om geometri och tredimensionella objekt samt vilka variationsmönster som synliggörs i lärarnas undervisning. Studien utgår från tidigare granskad forskning om geometriundervisning. Studiens undersökningar har genomförts på två olika skolor i två olika kommuner i södra Sverige där båda klasserna som varit en del av studien tillhört årskurs 6. Den datainsamling som gjorts bygger på fem genomförda observationer av två olika klasser samt intervjuer av undervisande lärare för dessa klasser. Studiens resultat visar bland annat att geometriundervisning där läromedel kompletteras med andra undervisningsmetoder såsom konkret material kan vara gynnande för elevers inlärning och för lärare vid undervisning om tredimensionella objekt.

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  • 32.
    Alexandra, Karlsson
    et al.
    Linnaeus University, Faculty of Social Sciences, Department of Education. Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Marija, Ljubomirovic
    Linnaeus University, Faculty of Social Sciences, Department of Education. Linnaeus University, Faculty of Technology, Department of Mathematics Education.
    Decimaltal i skolans värld2015Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Decimaltal uppfattas som ett komplicerat ämne, både för lärare och elever. Syftet med uppsatsen är att svara på frågan hur verksamma lärare arbetar med decimaltal i sin undervisning i årskurs 5. Uppsatsen är baserad på tre frågor gällande undervisningen om decimaltal. För att svara på frågorna är arbetet lutat mot teorier som handlar om olika matematiska aspekter kopplat till decimaltal. De metoder som använts för insamlande av data i denna kvalitativa studie är genom observationer av undervisning och lärarintervjuer. Med hjälp av teorierna och insamlade data kan vi läsa i resultatet om lärarnas uppfattningar om undervisning av decimaltal. De intervjuade lärarna påtalar att elever att elever har svårigheter med att förstå hur heltal och decimaltal fungerar.

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  • 33.
    Algotsson, Sarah
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Tror jag att jag kan det här?: En kvantitativ studie om elevers tilltro till sin egen matematiska förmåga i relation till faktisk prestation i metod-och problemlösningsuppgifter  2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This quantitative study focuses on how students perceive their own mathematical ability, what degree of confidence students have in their ability and how they perform in mathematical tasks that focuses on method and problem solving ability. The literature underlying the study is based on the importance of believing in your own ability, the ability to assess yourself and your ability, and the importance of mathematics to maintain and create opportunity to develop self-perception and confidence in your own ability. The research method used to answer the questions of the study is of a quantitative nature and consists of a self-assessment form that aims to visualize the students' degree of confidence in their own mathematical ability and a mathematics test where students solve method and problem solving tasks. The dissolution rate of the different types of tasks is analyzed in relation to the students' degree of confidence. The study is pervaded by a social psychological perspective and the result is theorized by starting from the social psychological theory of self-efficacy as well as symbolic interactionism. To analyze the relationships, the material has also been analyzed from a statistical perspective, using the SPSS analyzing tool. The result of the study shows that there seems to be a connection between the students' degree of confidence in their mathematical ability and how they perform in both method and problem solving tasks.

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  • 34.
    Algotsson, Sarah
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Uusitalo, Ellen
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Matematik, för vem?: En studie om interaktion mellan lärare och elever samt elevers uppfattning om matematik och vem som är matematisk sett ur ett genusperspektiv2018Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Denna kvalitativa studie syftar till att försöka synliggöra lärares interaktion med flickor och pojkar i en matematikundervisningssituation genom att observera interaktionen som sker mellan lärare-flickor och lärare-pojkar med syfte att synliggöra likheter och skillnader i interaktionen. Studien syftar även till att försöka synliggöra hur flickor och pojkar talar om matematik och om någon som är matematisk genom att intervjua elever och ställa det i relation till hur eleverna talar om sig själva som matematiker. För att svara på studiens första frågeställning användes ett observationsschema, och för att svara på studiens andra frågeställning användes en intervjuguide. Studiens teoretiska utgångspunkter har använts för att skapa både observationsschema och intervjuguide. De teoretiska utgångspunkterna är symbolisk interaktionism, diskursanalys och feministisk teori. Dessa teoretiska utgångspunkter utgör centrala delar av såväl analys av empiri som av diskussionen. För att analysera empirin konstruerades en analysmodell som är baserad på begrepp från diskursanalys och symbolisk interaktionism.  Utifrån resultatet framgick att pojkar överlag gavs mest utrymme av lärare i matematikundervisningssituationerna. Flickor och pojkar beskriver den som är matematisk med tre huvuddrag; snabb, har rätt och förstår. Flickor och pojkar verkar i studien överens om att pojkar passar mer in på bilden av vem som är matematisk då pojkar beskrivs mer som beskrivningen av huvuddragen än vad flickor gör.

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  • 35.
    Algulin, David
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Sandberg, Jesper
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Hur undervisar lärare elev- respektive lärarcentrerat i matematik?: En kvalitativ intervjustudie om hur lärare i årskurs 4-6 undervisar elev- respektive lärarcentrerat om triangelns area.2022Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Denna kvalitativa intervjustudie syftar till att undersöka hur elev- och lärarcentrerad undervisning kommer till uttryck i årskurserna 4 till 6. Empirin samlades in genom semistrukturerade intervjuer där lärarna fick berätta om sina pedagogiska planeringar för matematikområdet areaformeln för triangeln. I studien intervjuades totalt tio verksamma matematiklärare, och empirin analyserades sedan utifrån det teoretiska ramverket framskrivet av Trigwell, där undervisning kan kategoriseras som elev- eller lärarcentrerad. I resultatet framkom en stor variation inom en av nivåerna vilket förhandledde att två nya kategorier inom nivån skapades, och genom det utvecklades teorin för att möta studiens behov. Slutsatsen är att både elev- och lärarcentrerad undervisning kommer till uttryck med en stor variation och det framträder en bild av att det finns behov av utbildning inom området.

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  • 36.
    Algulin, David
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Sandberg, Jesper
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Induktiva och deduktiva arbetssätt inom matematik: En systematisk litteraturstudie om hur induktiva och deduktiva arbetssätt kan påverka elevers matematiska förståelse2021Independent thesis Basic level (university diploma), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Denna systematiska litteraturstudie syftar till att undersöka hur induktiva eller deduktivaarbetssätt i undervisning påverkar elevers förståelse för matematiska innehåll samt vilka föroch nackdelar det finns med respektive. Studiens frågeställningar grundar sig i egnaerfarenheter och utifrån observation på skolor, där vi mött elever med bristande matematiskförståelse. Vi har då uppmärksammat att lärare återkommande fokuserar undervisningen påutantillkunskap, och i hög grad bearbetar matematiska innehåll med deduktiva arbetssätt.Observationerna utgjorde grunden till en hypotes om att det finns ett samband mellan eleversbristande förståelse och deduktiv undervisning som fokuserar på utantillkunskap. I studiengranskas tidigare forskning genom att tio utvalda vetenskapliga artiklar kategoriseras utifrånteoretiska perspektiv och dess innehåll tematiseras utifrån framgångsfaktorer för eleverslärande. Studiens resultat med utgångspunkt i de granskade artiklarna tyder på attarbetssättets induktiva eller deduktiva karaktär är av mindre betydelse för eleversmatematiska förståelse. Slutsatsen blir således att de identifierade framgångsfaktorerna ärmer adekvata för elevers matematiska förståelse. 

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  • 37.
    Alice, Reinaudo
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Empirical testing of pseudo random number generators based on elliptic curves2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    An introduction on random numbers, their history and applications is given, along with explanations of different methods currently used to generate them. Such generators can be of different kinds, and in particular they can be based on physical systems or algorithmic procedures. The latter type of procedures gives rise to pseudo-random number generators. Specifically, several such generators which are based on elliptic curves are examined. Therefore, in order to ease understanding, a basic primer on elliptic curves over fields and the operations arising from their group structure is also provided. Empirical tests to verify randomness of generated sequences are then considered. Afterwards, there are some statistical considerations and observations about theoretical properties of the generators at hand, useful in order to use them optimally. Finally, several randomly generated curves are created and used to produce pseudo-random sequences which are then tested by means of the previously described generators. In the end, an analysis of the results is attempted and some final considerations are made.

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  • 38.
    All Carreberg, Susanna
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Karlsson, Lina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Tal och tanke: hur problemlösningsdiskurser förändras genom samarbete2019Independent thesis Advanced level (degree of Master (One Year)), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med denna studie är att beskriva processen som sker när elever arbetar tillsammans med en problemlösningsuppgift de tidigare inte kunnat lösa vid enskilt arbete. Fokus har varit på förändrad användning av Sfards (2008) nyckelbegrepp: ämnesspecifika ord, visuella mediatorer, rutiner och berättelser samt vilka diskursförändringar som synliggjorts. Studien är kvalitativ och empirin har samlats in genom observationer av problemlösningsarbetet, ljudinspelningar under pararbeten och bildupptagningar av elevmaterialet. Totalt tio observationer av gemensamt arbete genomfördes och transkriberades och av dessa djupanalyserades fem transkriberingar med hjälp av flödesscheman och Sfards (2008) nyckelbegrepp. Resultatet visar att eleverna i studien använde fler nyckelbegrepp vid den gemensamma problemlösningen och därmed ingick i diskursförändringar som bidrog till att föra problemlösningen framåt. Visuella mediatorer och användningen av tid visade sig vara viktiga aspekter för användning av fler nyckelbegrepp och förändring av diskurser.

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  • 39.
    Almgren, Annika
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Vilka erfarenheter kan ligga till grund för valet att gå en spetsutbildning i matemaik2016Independent thesis Advanced level (degree of Master (One Year)), 40 credits / 60 HE creditsStudent thesis
    Abstract [sv]

    Denna undersöknings syfte var att ge ett elevperspektiv på vilka faktorer som kan ligga till grund för valet att gå en spetsutbildning i matematik samt om man kan skönja gemensamma uttryck i vad som kan ha varit avgörande för detta val.

    Följande forskningsfrågor har legat till grund för studien:

    • Vilka faktorer uttrycker elever för valet att gå en spetsutbildning i matematik?

    • Vilken syn på matematik och matematikundervisning uttrycks hos dessa elever?

    • Går det att finna några kopplingar mellan de faktorer eleverna uttrycker för sitt val att gå en spetsutbildning i matematik och deras uttryckta syn på matematik och matematikundervisning?

       

    En hermeneutiska tolkningsansats användes och en enkätundersökning gjord på elever på spetsutbildningar i årskurs 7 låg till grund som data. Resultaten visade att den elev som väljer att gå en spetsutbildning i matematik kan ha grundat sina val på en mängd skiljda faktorer men det finns också faktorer som visade sig finnas hos majoriteten av dem. En generell bild av en elever som väljer att gå en spetsutbildning i matematik gör det för sin lusta att lära och att de söker utmaningar i ett ämne de inte nödvändigtvis har som favoritämne men känner en stor tillfredställelse att ägna sig åt. Ofta finns det föräldrar som uppmuntrar och är delaktiga i sina barns utbildning och det är i större utsträckning syskon som haft påverkan än kompisar. Användbarhet av matematik är inte alltid synlig för eleven i den egna vardagen men en majoritet anser att ämnet är en mycket viktig del i dagen samhälle.

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  • 40.
    Almquist, Rebecka
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Lindgren, Josefine
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Multiplikation: användningen av och uppfattningar om olika metoder inom multiplikation2017Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Multiplikation är ett av de fyra räknesätten inom matematik som elever ska utveckla kunskap och förståelse inom. Utifrån lärarens undervisning ska eleverna ges möjlighet att i slutet av årskurs 6 kunna behärska olika metoder inom multiplikation. Syftet med studien är att urskilja vilka metoder inom multiplikation som är vanligast förekommande i två stycken årskurs 5-klasser samt vilka metoder som matematikläraren för dessa klasser använder mest i genomgången av multiplikation. Syftet är även att försöka tolka olika elevers uppfattningar inom dessa metoder. Studien genomfördes med hjälp av en kvalitativ analys utifrån en fenomenografisk ansats.

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  • 41.
    Alodjants, A. P.
    et al.
    ITMO Univ, Russia.
    Tsarev, D. V.
    ITMO Univ, Russia.
    Avdyushina, A. E.
    ITMO Univ, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Boukhanovsky, A. V.
    ITMO Univ, Russia.
    Quantum-inspired modeling of distributed intelligence systems with artificial intelligent agents self-organization2024In: Scientific Reports, E-ISSN 2045-2322, Vol. 14, no 1, article id 15438Article in journal (Refereed)
    Abstract [en]

    Distributed intelligence systems (DIS) containing natural and artificial intelligence agents (NIA and AIA) for decision making (DM) belong to promising interdisciplinary studies aimed at digitalization of routine processes in industry, economy, management, and everyday life. In this work, we suggest a novel quantum-inspired approach to investigate the crucial features of DIS consisting of NIAs (users) and AIAs (digital assistants, or avatars). We suppose that N users and their avatars are located in N nodes of a complex avatar - avatar network. The avatars can receive information from and transmit it to each other within this network, while the users obtain information from the outside. The users are associated with their digital assistants and cannot communicate with each other directly. Depending on the meaningfulness/uselessness of the information presented by avatars, users show their attitude making emotional binary "like"/"dislike" responses. To characterize NIA cognitive abilities in a simple DM process, we propose a mapping procedure for the Russell's valence-arousal circumplex model onto an effective quantum-like two-level system. The DIS aims to maximize the average satisfaction of users via AIAs long-term adaptation to their users. In this regard, we examine the opinion formation and social impact as a result of the collective emotional state evolution occurring in the DIS. We show that generalized cooperativity parameters G(i), i=1,...,N introduced in this work play a significant role in DIS features reflecting the users activity in possible cooperation and responses to their avatar suggestions. These parameters reveal how frequently AIAs and NIAs communicate with each other accounting the cognitive abilities of NIAs and information losses within the network. We demonstrate that conditions for opinion formation and social impact in the DIS are relevant to the second-order non-equilibrium phase transition. The transition establishes a non-vanishing average information field inherent to information diffusion and long-term avatar adaptation to their users. It occurs above the phase transition threshold, i.e. at G(i)>1, which implies small (residual) social polarization of the NIAs community. Below the threshold, at weak AIA-NIA coupling (G(i)<= 1), many uncertainties in the DIS inhibit opinion formation and social impact for the DM agents due to the information diffusion suppression; the AIAs self-organization within the avatar-avatar network is elucidated in this limit. To increase the users' impact, we suggest an adaptive approach by establishing a network-dependent coupling rate with their digital assistants. In this case, the mechanism of AIA control helps resolve the DM process in the presence of some uncertainties resulting from the variety of users' preferences. Our findings open new perspectives in different areas where AIAs become effective teammates for humans to solve common routine problems in network organizations.

  • 42.
    Alodjants, Alexander P.
    et al.
    ITMO Univ, Russia.
    Avdyushina, Anna E.
    ITMO Univ, Russia.
    Tsarev, Dmitriy V.
    ITMO Univ, Russia.
    Bessmertny, Igor A.
    ITMO Univ, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Quantum Approach for Contextual Search, Retrieval, and Ranking of Classical Information2024In: Entropy, E-ISSN 1099-4300, Vol. 26, no 10, article id 862Article in journal (Refereed)
    Abstract [en]

    Quantum-inspired algorithms represent an important direction in modern software information technologies that use heuristic methods and approaches of quantum science. This work presents a quantum approach for document search, retrieval, and ranking based on the Bell-like test, which is well-known in quantum physics. We propose quantum probability theory in the hyperspace analog to language (HAL) framework exploiting a Hilbert space for word and document vector specification. The quantum approach allows for accounting for specific user preferences in different contexts. To verify the algorithm proposed, we use a dataset of synthetic advertising text documents from travel agencies generated by the OpenAI GPT-4 model. We show that the "entanglement" in two-word document search and retrieval can be recognized as the frequent occurrence of two words in incompatible query contexts. We have found that the user preferences and word ordering in the query play a significant role in relatively small sizes of the HAL window. The comparison with the cosine similarity metrics demonstrates the key advantages of our approach based on the user-enforced contextual and semantic relationships between words and not just their superficial occurrence in texts. Our approach to retrieving and ranking documents allows for the creation of new information search engines that require no resource-intensive deep machine learning algorithms.

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  • 43.
    Alodjants, Alexander P.
    et al.
    IIMO Univ, Russia.
    Bazhenov, A. Yu
    IIMO Univ, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Bukhanovsky, A. , V
    ITMO University, Russia.
    Mean-field theory of social laser2022In: Scientific Reports, E-ISSN 2045-2322, Vol. 12, no 1, article id 8566Article in journal (Refereed)
    Abstract [en]

    In this work we suggest a novel paradigm of social laser (solaser), which can explain such Internet inspired social phenomena as echo chambers, reinforcement and growth of information cascades, enhancement of social actions under strong mass media operation. The solaser is based on a wellknown in quantum physics laser model of coherent amplification of the optical field. Social networks are at the core of the solaser model; we define them by means of a network model possessing power-law degree distribution. In the solaser the network environment plays the same role as the gain medium has in a physical laser device. We consider social atoms as decision making agents (humans or even chat bots), which possess two (mental) states and occupy the nodes of a network. The solaser establishes communication between the agents as absorption and spontaneous or stimulated emission of socially actual information within echo chambers, which mimic an optical resonator of a convenient (physical) laser. We have demonstrated that social lasing represents the second order nonequilibrium phase transition, which evokes the release of coherent socially stimulated information field represented with the order parameter. The solaser implies the formation of macroscopic social polarization and results in a huge social impact, which is realized by viral information cascades occurring in the presence of population imbalance (social bias). We have shown that decision making agents follow an adiabatically time dependent mass media pump, which acts in the network community reproducing various reliable scenarios for information cascade evolution. We have also shown that in contrast to physical lasers, due to node degree peculiarities, the coupling strength of decision making agents with the network may be enhanced root < k > times. It leads to a large increase of speed, at which a viral message spreads through a social media. In this case, the mass media pump supports additional reinforcement and acceleration of cascade growth. We have revealed that the solaser model in some approximations possesses clear links with familiar !sing and SIS (susceptible-infected-susceptible) models typically used for evaluating a social impact and information growth, respectively. However, the solaser paradigm can serve as a new platform for modelling temporal social events, which originate from "microscopic" (quantum-like) processes occurring in the society. Our findings open new perspectives for interdisciplinary studies of distributed intelligence agents behavior associated with information exchange and social impact.

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  • 44.
    Alodjants, Alexander
    et al.
    ITMO Univ, Russia.
    Zacharenko, Peter
    ITMO Univ, Russia.
    Tsarev, Dmitry
    ITMO Univ, Russia.
    Avdyushina, Anna
    ITMO Univ, Russia.
    Nikitina, Mariya
    ITMO Univ, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Boukhanovsky, Alexander
    ITMO Univ, Russia.
    Random Lasers as Social Processes Simulators2023In: Entropy, E-ISSN 1099-4300, Vol. 25, no 12, article id 1601Article in journal (Refereed)
    Abstract [en]

    In this work, we suggest a quantum-like simulator concept to study social processes related to the solution of NP-hard problems. The simulator is based on the solaser model recently proposed by us in the framework of information cascade growth and echo chamber formation in social network communities. The simulator is connected with the random laser approach that we examine in the A and D-class (superradiant) laser limits. Novel network-enforced cooperativity parameters of decision-making agents, which may be measured as a result of the solaser simulation, are introduced and justified for social systems. The innovation diffusion in complex networks is discussed as one of the possible impacts of our proposal.

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  • 45.
    Alriksson, Madeleine
    Linnaeus University, Faculty of Engineering and Technology, Department of Mathematics Education.
    Muntlig bedömning: Med fokus på elevers representationer2013Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Muntlig bedömning är, från och med höstterminen 2011, något som alla matematiklärare inom gymnasieskolan kommer att få genomföra då en muntlig del läggs som obligatorisk för alla elever inom årskurs 1. Syftet med den här studien är därför att konstruera kriterier som lärare kan använda som hjälp vid muntlig bedömning. Fokus kommer att ligga på elevers representationsformer och transformationer däremellan utifrån ett sociokulturellt perspektiv. Elevgrupper filmades då de löste en problemlösningsuppgift och analyserades utifrån ett begreppsligt ramverk. Resultatet visar att elevers transformationer mellan representationer visar både missuppfattningar och förståelse beroende på hur dessa transformationer ter sig. Elever som obehindrat lyckas vandra mellan olika representationer visar på god förståelse för det matematiska innehållet. Även elevers förmåga att skapa sig ett multimodalt arbetssätt visar sig, för läraren, vara värd att uppmärksamma. 

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  • 46.
    Alstad, Edgar
    et al.
    Nord University, Norway.
    Berre, Maren
    Nord University, Norway.
    Nilsson, Per
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Exploring spherical units as perceptual clues in enumerating 3D arrays2024In: Mathematics Education Research Journal, ISSN 1033-2170, E-ISSN 2211-050X, Vol. 36, p. 671-693Article in journal (Refereed)
    Abstract [en]

    This study continues an investigation of how spherical units, compared to cubical units, can facilitate students’ units-locating and organizing units in composites. We analyze how Norwegian grade 3 students enumerate 3D arrays with cubical and spherical units. Our results show how spherical units can act as perceptual clues that facilitate cognitive processes, underlying students’ strategies in the enumeration of 3D arrays. In particular, the results show how spherical units facilitate the units-locating process, which, in turn, supports processes of organizing-by-composites and spatial structuring of the array, in the action of developing a proper iterative strategy such as layer-based thinking.

  • 47.
    Al-Talibi, Haidar
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Differentiable Approximation of Diffusion Equations Driven by α-Stable Lévy Noise2013In: Brazilian Journal of Probability and Statistics, ISSN 0103-0752, E-ISSN 2317-6199, Vol. 27, no 4, p. 544-552Article in journal (Refereed)
    Abstract [en]

    Edward Nelson derived Brownian motion from Ornstein-Uhlenbeck theory by a scaling limit. Previously we extended the scaling limit to an Ornstein-Uhlenbeck process driven by an α-stable Lévy process. In this paper we extend the scaling result to α-stable Lévy processes in the presence of a nonlinear drift, an external field of force in physical terms.

  • 48.
    Amanda, Axelsson
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Bengtsson, Malin
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Hur löser vi det med bråk?: En läromedelsanalys med syfte att analysera två läromedels uppbyggnad och struktur med avseende på hur de väljer att framställa bråk i årskurs tre2019Independent thesis Advanced level (degree of Master (Two Years)), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I många klassrum används läromedel dagligen, men vad innebär det egentligen att använda ett läromedel och vilka krav ställer det på elever och lärare? Syftet med denna studie är att analysera två olika läromedels uppbyggnad och struktur med avseende på hur de väljer att framställa bråk i årskurs tre. För att skapa en förståelse för hur olika händelser och fenomen hänger samman har studien använt sig av ett teoretiskt perspektiv, variationsteorin. Användandet av variationsteorin har på så vis bidragit till att huvudfokus har legat på vikten av en varierad undervisning. De båda läromedlen har därför analyserats med avseende på vilka typer av uppgifter som förekommer, vilka geometriska figurer som används samt vad eleverna faktiskt får öva på i relation till Lgr11. Att välja ett läromedel är ett moment som bör göras med såväl efter-, som omtanke. Studiens resultat påvisar att de båda läromedlen är lämpliga att använda i matematikundervisningen i årskurs tre, men att de förbereder eleverna på olika sätt. De båda läromedlen behöver kompletteras på olika sätt, med allt från minilektioner, genomgångar och extra uppgifter, vilket i sin tur bidrar till att undervisningen inte enbart kan förlita sig på att läromedlet ska förmedla allt.

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  • 49.
    Anashin, Vladimir
    et al.
    Moscow MV Lomonosov State Univ, Fac Computat Math & Cybernet, Moscow 119991, Russia.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Ergodicity criteria for non-expanding transformations of 2-adic spheres2014In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 34, no 2, p. 367-377Article in journal (Refereed)
    Abstract [en]

    In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems < f; S2-r (a)> on 2-adic spheres S2-r (a) of radius 2(-r), r >= 1, centered at some point a from the ultrametric space of 2-adic integers Z(2). The map f: Z(2) -> Z(2) is assumed to be non-expanding and measure-preserving; that is, f satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and f preserves a natural probability measure on Z(2), the Haar measure mu(2) on Z(2) which is normalized so that mu(2)(Z(2)) = 1.

  • 50.
    Anashin, Vladimir
    et al.
    Lomonosov Moscow State University.
    Khrennikov, Andrei
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Yurova, Ekaterina
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    T-functions revisited: new criteria for bijectivity/transitivity2014In: Designs, Codes and Cryptography, ISSN 0925-1022, E-ISSN 1573-7586, Vol. 71, no 3, p. 383-407Article in journal (Refereed)
    Abstract [en]

    The paper presents new criteria for bijectivity/transitivity of T-functions and a fast knapsack-like algorithm of evaluation of a T-function. Our approach is based on non-Archimedean ergodic theory: Both the criteria and algorithm use van der Put series to represent 1-Lipschitz p-adic functions and to study measure-preservation/ergodicity of these.

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